Milwaukee Mayor Tom Barrett, right, told supporters during a campaign stop April 30, in Eau Claire, Wis., that, if elected in the June gubernatorial recall election, he would focus on creating jobs and ending the division created by GOP Gov. Scott Walker. Barrett is one of four Democrats running in the primary on Tuesday, May 8.

In Tuesday’s primary, Wisconsin voters will determine which Democrat will face off against Gov. Scott Walker (R) in the state’s recall election in June.

The state has an open primary system that does not require voters to declare a party affiliation. This creates the possibility that Republicans may try to sabotage the vote by casting ballots for Kathleen Falk, a former Dane County executive. According to polls, she is the weaker candidate in a contest against Governor Walker. Milwaukee Mayor Tom Barrett, the other leading Democratic candidate, is polling in a dead heat against Walker.

In the end, Tuesday could come down to independent voters. Thirty-six percent of those voting Tuesday identify themselves as independent, according to the polling conducted by Marquette University Law School in Milwaukee.

Independents have recoiled from the partisan bickering that has deadlocked Wisconsin politics since Walker took office in 2011 and pushed through legislation that weakened the collective-bargaining power of public-sector unions. But how they’ll vote on Tuesday could be complicated, because there is evidence of fracture among both Republican-leaning and Democratic-leaning independents: There are some Democratic-leaning independents who are angered that the continued round of recall elections is draining state resources, and there are some Republican-leaning independents who feel Walker overreached his mandate.

“It doesn’t look like most [Republicans] are crossing over to cause mischief in the Democratic primary, but it doesn’t mean that Republicans are strongly dissatisfied with Scott Walker either,” Mr. Franklin says.

Republicans are most likely to vote for Mayor Barrett even though he stands the greatest chance of defeating Walker in the June 5 general election, notes Franklin, citing polling.

Voter turnout on Tuesday is expected to fall shy of that in 1952, the highest primary turnout on record in Wisconsin, according to state election officials. Between 30 to 35 percent of the voting-age population, or as many as 1.5 million people, are expected to show up at the polls. In 1952, voter turnout reached 38.9 percent.

Despite the vitriol hurled against Walker over the past year by his opponents, removing him from office falls second to job creation as the primary motivation for voters to cast ballots. Nearly half of likely voters say that creating jobs is the most important factor in their voting decision, according to polls. Twenty-five percent say it’s simply to fire Walker.

Barrett and Ms. Falk are both capitalizing on Walker’s continued promise to create 250,000 jobs by the end of his term in 2015, saying it’s evidence he is out of touch with Wisconsin voters and has not made it a priority of his administration.

Wisconsin lost 23,900 jobs between March 2011 and March 2012, according to data released last month by the US Bureau of Labor Statistics. By comparison, no other state in the US lost more than 3,500 jobs.

However, neither Barrett nor Falk has made it clear how he or she would solve the state’s budget problems while at the same time rolling back tax cuts, restoring collective bargaining powers for unions, or canceling cuts that Walker made to BadgerCare Plus, the state’s health-care program.

Even though both candidates say they will ensure collective bargaining is a right of public-sector unions, they disagree on how to do it. Barrett favors a special legislative session, while Falk says he would simply veto any budget that does not restore collective-bargaining powers. Marquette polling shows that more than half of Tuesday’s primary voters favor Barrett’s approach.

To persuade independents to vote for a Democrat, the party will need to come up with policies that sound realistic in a State Capitol still ruled by a Republican majority, says Geoff Peterson, a political scientist at the University of Wisconsin in Eau Claire.

“Once Democrats pick a candidate and go toward the actual recall, that is where the policy stuff starts to become trickier,” Mr. Peterson says. Removing Walker from office may drive the Democratic base to the polls, but Democrats will still “need to win over enough independents ... and that’s where you run into that issue: Yes you got rid of Walker, and now what?”

Walker is framing the recall election as damaging to the state’s economic health, particularly job creation.

In remarks made to the Milwaukee Journal Sentinel last week, Walker said that if he loses, it will open the door to “recall ping-pong.”

“It will go back and forth. I don't think that's just bad for elections; it's bad for jobs,” he said.